Lucy Had $ 72 \$72 $72 , Which Is Nine Times As Much Money As Xavier Had. How Much Money Did Xavier Have? Select The Correct Solution Method Below, Representing Xavier's Money With X X X .A. 9 X = 72 9x = 72 9 X = 72 . Divide Both Sides By 9. Xavier Had

Introduction

In this problem, we are given that Lucy has $\$72$, which is nine times as much money as Xavier had. We need to find out how much money Xavier had. To solve this problem, we will use algebraic methods to represent Xavier's money with a variable and then solve for its value.

Step 1: Representing Xavier's Money with a Variable

Let's represent Xavier's money with a variable $x$. This means that the amount of money Xavier has is represented by the variable $x$.

Step 2: Setting Up the Equation

We are given that Lucy has $\$72$, which is nine times as much money as Xavier had. This can be represented by the equation:

$$9x = 72$$

In this equation, $9x$ represents the amount of money Lucy has, which is nine times the amount of money Xavier has.

Step 3: Solving for Xavier's Money

To solve for Xavier's money, we need to isolate the variable $x$ on one side of the equation. We can do this by dividing both sides of the equation by 9.

$$\frac{9x}{9} = \frac{72}{9}$$

This simplifies to:

$$x = 8$$

Therefore, Xavier had $\$8$.

Conclusion

In this problem, we used algebraic methods to represent Xavier's money with a variable and then solve for its value. We set up an equation based on the given information and solved for the variable $x$ by dividing both sides of the equation by 9. This resulted in the solution that Xavier had $\$8$.

Alternative Solution Methods

There are other ways to solve this problem, but the method we used is the most straightforward and efficient. Here are a few alternative solution methods:

• Dividing both sides by 9: This is the method we used in this solution. It involves dividing both sides of the equation by 9 to isolate the variable $x$.
• Using inverse operations: This method involves using inverse operations to isolate the variable $x$. For example, if we have the equation $9x = 72$, we can use the inverse operation of multiplication, which is division, to isolate the variable $x$.
• Using a calculator: This method involves using a calculator to solve the equation. For example, if we have the equation $9x = 72$, we can use a calculator to divide both sides of the equation by 9 to isolate the variable $x$.

Discussion

This problem is a classic example of a linear equation in one variable. It involves representing a variable with a value and then solving for that value using algebraic methods. The solution we used in this problem is the most straightforward and efficient method, but there are other ways to solve this problem as well.

Key Takeaways

• Representing a variable with a value is an important step in solving linear equations.
• Using algebraic methods, such as dividing both sides of an equation by a coefficient, is an effective way to solve linear equations.
• There are alternative solution methods, such as using inverse operations or a calculator, that can be used to solve linear equations.

Practice Problems

Here are a few practice problems that involve solving linear equations:

• If $x + 5 = 11$, solve for $x$.
• If $2x = 14$, solve for $x$.
• If $x - 3 = 7$, solve for $x$.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form:

ax + b = c

where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division. For example, if you have the equation 3x = 12, you can divide both sides of the equation by 3 to isolate the variable x.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to follow these steps:

1. Identify the operation that was used to combine the terms on the left-hand side of the equation.
2. Use the inverse operation to isolate the variable on one side of the equation.
3. Simplify the equation by combining like terms.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are constants, and x is the variable.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are constants, and x is the variable.

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula to solve a quadratic equation, you need to follow these steps:

1. Identify the values of a, b, and c in the quadratic equation.
2. Plug these values into the quadratic formula.
3. Simplify the equation by combining like terms.
4. Solve for x.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a system of linear equations is a set of two or more linear equations that are solved simultaneously.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to use the following methods:

1. Substitution method: This method involves substituting the expression for one variable from one equation into the other equation.
2. Elimination method: This method involves adding or subtracting the equations to eliminate one variable.
3. Graphing method: This method involves graphing the equations on a coordinate plane and finding the point of intersection.

Q: What is the substitution method?

A: The substitution method is a method of solving a system of linear equations by substituting the expression for one variable from one equation into the other equation.

Q: What is the elimination method?

A: The elimination method is a method of solving a system of linear equations by adding or subtracting the equations to eliminate one variable.

Q: What is the graphing method?

A: The graphing method is a method of solving a system of linear equations by graphing the equations on a coordinate plane and finding the point of intersection.

Conclusion

In this article, we have discussed the basics of solving linear equations, including the use of inverse operations, the quadratic formula, and the substitution, elimination, and graphing methods for solving systems of linear equations. We have also provided answers to frequently asked questions about solving linear equations.